A stepped automatic transmission for a vehicle is well known that engages/releases friction engagement devices to form a predetermined shift stage. For example, this corresponds to an automatic transmission described in Patent Document 1. In general, in such a stepped automatic transmission, for example, in response to determination of a rotation condition for performing a shift (e.g., any of vehicle speed, shift input rotation speed, engine rotation speed etc.) and a torque condition (e.g., any of transmission input torque, engine torque, or a value controlling the engine torque such as throttle valve opening degree, accelerator opening degree or an intake air amount, etc.), an inertia change amount is uniquely determined that is generated by a change in the transmission input rotation speed and a change in the engine rotation speed associated with the same type of shift in the stepped automatic transmission (i.e., a shift of the same shift type (e.g., upshift from one to two) in the stepped automatic transmission), i.e., a rotational change in an engine and a rotational change in a rotating member making up the stepped automatic transmission at the time of shift of the same type. Therefore, as described in Patent Document 1, the stepped automatic transmission has a clutch pressure of engagement devices to be responsible for the engine torque at the time of shift and a change in inertia associated with the shift (or a line pressure of a hydraulic circuit acting as an original pressure of the clutch pressure) set based on the engine torque and is controlled to avoid an excess or a shortage of the clutch pressure relative to the transmission input torque.